Question

There is a triangle ABC, comparison between the tan A: tan B: tan C = 1:2:3.
How to find AB:AC ?

Answer 1

In a triangle, tan A + tan B + tan C = tan A tan B tan C.

Answer 2

sinA/cosA : sinB/cosB : sinC:cosC

Answer 3

@blockcolder : then??

Answer 4

Let tan A=k, tan B=2k, tan C=3k.
From my previous reply, we have k+2k+3k=k*2k*3k
6k=6k^3
6k^3-6k=0
6k(k^2-1)=0
k=-1, 0, 1
k=0 would mean tan A=0 and A=0, so this is impossible.
k=-1 would mean tan A=-1 and A=-pi/4 so again this is impossible.
k=1 would mean tan A=1 and A=pi/4.

Answer 5

then tan B=2.
so B is 63,43.

then tan C=3
so C is 71.565

is it correct?

Answer 6

Now use the law of sines to find the ration AB:AC.